Rote Learning Vis-à-vis Physical Comprehension

Manto writes "and who made made his wealth through dedication, hard work and devotion "

Wealth in our world is not made through "dedication, hard work and devotion", that is the feel-good mythology generated by the elite not only to justiy their own outrageous wealth disparity with the masses but also to motivate their slaves into putting in extra effort. Rather, in our world, wealth is made through manipulation (of the Jinnah kind), whoring your morals to the elite (of the Jinnah kind) and going through their institutions that shape and mold you so that you always think in their terms and of them as superiors (of the Jinnah kind).

Myself, I reject that enslavement to the white man and his institutions. I am for people power and not the petty- feudalism (like the petty bourgeoisie) of the Jinnah kind, with pipe dreams of the Ata Turk kind....

Manto writes ".... is suddenly a "feudal".a'

Having a feudalistic mentality has nothing to do with being a born feudal, your dimwit mind that is busy with man-worship wont understand that. Jinnah subverted democracy with his holier than thou, dicatatorship to benefit the West in the Ata Turk fashion, I on the other hand want to restore it by making the poor masses all-powerful, they certainly have greater knowledge of their daily lives and what affects them than implants like the MAJ who ran off to London to be a slave to his masters....

How many times do I have to knock off your ridiculous arguments in support of a self-styled, arrogant, selfish fool that caused death and destruction in our lands for your "faith" in the Church of MAJ to be shaken?


Chalta writes:"Masadi, let me guess, WRM handed your head on a platter with dismissing your knuckleheaded views with sharp smackdowns and genuine wit. "

Those are your wet-dreams, the meeting is still to take place and my knowledge of the issues is based on real research by real social scientists not whores who have tabulated bs to prove the unprovable, i.e. US benevolence in foreign policy. The victims of that foreign policy, those living in our parts of the world, social scientist or not can easily cut through that crap.....

So now Mahomed Ali Jinnah... the son of a small time Karachi Khoja merchant ... who spent his early youth in poverty but dignity after his father's demise... and who made made his wealth through dedication, hard work and devotion which is legendary and acknowledged by all of his colleagues and opponents.... is suddenly a "feudal".

Beautiful.

The biggest subverters of democracy are people like you Mr. Asadi... fascists trying to be populists. Trying spinning your god awfull theories in public and you would be lynched by the same people whose cause you claim to champion.

Masadi, let me guess, WRM handed your head on a platter with dismissing your knuckleheaded views with sharp smackdowns and genuine wit.

Alas..when faced with logic and the truth. I am sure yu hurled a few epiteths against the zionis capitalist corporate machinery and everyone laughed at you.

Walter Russell Mead of the CFR (Council on Foreign Relations) is in town trying to show the "benevolence" of US Foreign Policy......As cultural technician of the US elite he is employed to promote barbarism garbed in fine silk thread, draped with the finest perfume, "intellectual (BS) thinking" at its best... Boy is he in for a grilling during the Q&A session....let's see how his fat A$$ responds....

"Indeed we hurl the truth against falsehood and its knocks out its intellect and it vanishes clear away...." (Quran)

Manto writes "Now how many times are you going to repeat the thing about Government College. I understand that your application for employment there was never accepted."

As many times as it takes to get people here to understand how low you can get, and how infantile you are in your thinking that reduces you to such "threats" when you don't agree with other people's pov. It also explains how feudalistic you are in your outlook (like MAJ) when you invoke your "connections" in high places that would circumvent a person's merit in making decisions, precisely what is keeping this nation down (and subverting democracy in the tradition of the MAJ).

Khuram writes "I think "critical method" is the "tool" which helps in the development of "intellectual understanding".


No, Critical understanding transcends the so-called "intellectual understanding" which more often than not is understanding that is circumscribed by (i.e. restricted by) narrow methodology or the most favored paradigm at whatever time. It is understanding that is affected by academic culture and its dominant themes. It is to be avoided by all those who seek true, unadulterated, non-pretentious knowledge...

Manto writes ""is even more good."

Makes sense why your application for employment at GC met with resistance. "

Einstein, learn how to read first, those were Khuram's words not mine, I was only quoting them...those are still better than your dimwit man-worship...By the way my application was not "rejected" by GC. I can get in there today if I want to...

Khuram writes "And I don't even want to degrade "mere speculation". "

Mere speculation needs to be checked, imagination should be guided by facts or you get a whole bunch on nonsense that you cannot work with

Manto writes ""is even more good."

Makes sense why your application for employment at GC met with resistance. "

Einstein, learn how to read first, those were Khuram's words not mine, I was only quoting them...those are still better than your dimwit man-worship...By the way my application was not "rejected" by GC. I can get in there today if I want to...

Khuram writes "And I don't even want to degrade "mere speculation". "

Mere speculation needs to be checked, imagination should be guided by facts or you get a whole bunch on nonsense that you cannot work with

VRV: #56

This is the kind of feedback I was expecting from the readers. I wanted to understand if the current methods of teaching have changed (they ought to be) for the better from the old ones (say of 1950s). If yes, in what significant manner they are different.
Thanks for your input.

Mohammad Gill

“You are explaining theory with real-life examples and that makes understanding the theory very easy.....”


This struck me well and this was my dilemma and I always pestered my mathes teacher/lecturer/professors abt this & I never got my answers but followed the flock in solving the mathematical problems...almost mechanical approach to mathematics.....I think it's still the case now in many schools in India.

I was more puzzled to understand the underlying theroy (or examples) than the ways to answer vector algebra or vector calculus. Same with spherical trigonometry in later years. It never made sense to me in college days & the teachers were never interested to explain me/us why?

Good artilce to read Dr. Gill.

"is even more good."

Makes sense why your application for employment at GC met with resistance.

Masadi mian,

That was a lame answer as usual.

Now how many times are you going to repeat the thing about Government College. I understand that your application for employment there was never accepted.

My point however was never a threat to you... you kept accusing me of "deleting" your articles from Chowk because I apparently owned it.

-YLH

@ masadi #51

I think "critical method" is the "tool" which helps in the development of "intellectual understanding".

And I don't even want to degrade "mere speculation". Mere speculation also can lead to many new testable hypothesises. Then "scientific research method" can take those new hypothesises as it's input in the process of creation of new factual, valid and empirical knowledge.

regards!

Madani sahib thanks for your continual support, may Allah take you to ever higher planes of learning...

Khuram writes "But "Intellectual Understanding" is even more good. With "practical understanding", you just "practically implement" already existing theories. But with "intellectual understanding", you invent and make new theories!"

Actually it is "critical" understanding that takes existing theories, practical empirical evidence and then critically analyze that to combine it into workable/reasonable theories. But Gill wouldn't know becauce he himself, as his work shows, can only produce tape-recorderesque renditions with zero original intellect involved, like a damn calculator that tabulates entries and spits out that same thing in summary form.

Pure intellectual understanding of the philosopher kind is also misleading, as C. W. Mills said facts without a connecting theory are mere bits of information, and a theory without facts is mere speculation.....

The key is being skeptical of existing knowledge, being careful and systematic with the facts, and at the same time not being overly concerned with existing methods or concepts but having the imagination to invent new ones that mesh facts in ways that best explain them. But when a-holes like Gill and Co censor my articles and then write ones with titles borrowed from its text, you don't expect them to have any concern for knowledge or truth...

In addition to #49, I'd like to add the following for Manto:

" ..any other questions about the poll you rat, that are not accompanied with threats to get me fired from my job (at your imagined institution)?"

Manto writes "Masadi mian,

What about 43% in India? Is there a Church of MAJ there as well? "

No, the Church of MAJ operates in Pakistan and is not that well organized elsewhere. Regarding the 43% in India, those people would probably give a 45% Or higher approval rating to Daffy Duck, Mickey Mouse and the gang, to them "approval" of "MAJ" figures with those other prominent loony (tunes) characters...

Gill Sahib,

Nice to read this article. You have highlighted the superiority of practical comprehension over rote memorization. Obviously I have to agree with it. But in addition, I recognize another form of understanding which, I think, is superior to even practical comprehensions. I can share my following article which can explain my view in detail. This is one of my early writings so it can lack maturity of expression:

Practical and Intellectual Understanding

http://khuram.wordpress.com/2006/08/23/practical-and-intell ectual-understanding/

Practical Understanding is very good. But "Intellectual Understanding" is even more good. With "practical understanding", you just "practically implement" already existing theories. But with "intellectual understanding", you invent and make new theories! I have explained this point in my above-referred article.

regards!

Masadi mian,

What about 43% in India? Is there a Church of MAJ there as well?

We went through the discussion in detail and you failed to answer my points. So there is no point really in going in circles. You are utterly incapable of civilised academic dialogue based on facts.

Manto writes "Masadi mian,

An Indian poll recently conducted polls in Pakistan and India. One poll was about the founding fathers:

Jinnah's approval ratings in Pakistan 97% in India 43 %"

One things third rate lawyers should never do is throw out polls to social scientists as "proof". What kind of nonsense is this "approval rating"- approving of what? Of course they are going to approve just like the poll that Zia ul Haq conducted asking Pakistani's if they "wanted Islam"- what were they going to say? That the Church of MAJ has taboo attached with rejection is why you get these high poll numbers, dig a little deeper with REAL questions and you'll get to know just how deep the resentment is with lackeys of the West...

Masadi the genius writes:

"Yes, I am for real and I am the worst nightmare of a-holes of the West"

Masadi mian,

An Indian poll recently conducted polls in Pakistan and India. One poll was about the founding fathers:

Jinnah's approval ratings in Pakistan 97% in India 43 %

Gandhi's approval ratings in Pakistan 29% in India 85%

So your wishes are not going to come true.

Your failure to argue with facts and to repeat the illogic of the Mullah freaks who called Jinnah kafir-e-Azam in the 1940s shows your desperation.

So keep repeating your lies. Pakistanis are done believing liars like you who are their biggest enemies. And I speak for the common man... not you- a third rate reject.

Re: # 41 sorry physical / visual problems creeping up
The fist line from King Lear is wrongly written , so all lines, it has good rhyme
"oldest have born most
We that are young
shall never see so much
Nor live so long" Albany ( King Lear)"
what a poetic prose style writing I read when,young and then always remembered

Re: # 15
Study , real analysis goldburg than name calling Masadi.

Re: # 28 Masadi is real. People can read his book if you want to become free from western domination mentally.
Mr. Masadi you thoughts are right. I asked you to write about G man and you and I agree. ( As you know I have disagreed with you some times).
Even with all slander and criticism by Nanto man
I just felt about G man as in KingLear, Kinglear and her ungrateful
" Oldest have bosrn most
We that are young
Shall never see so much
Nor live so long" Albany ( King Lear- Bill Shakesare)
To my surprise you can find same echo in what Einsten said about G man after he had departed.

Re: # 32
Whatever I wrote supporting you is rejected so I do not want to waste my time. In usa heard is fast PhD programmes just like fast food at 3rd rate and 4rate univs. It is absurd and laughable when they talk of producing 1000 Phds per year who are mostly worthless like fast food burgers which is imposed dirty and unhealthy food imposed on brown and dark people by american food factories. They should ban them. They produce 4000 calories worth food per person in usa. 2400 calaries needed consume all those calories produced by food factories resulting in fat and obase population. As you said slavary pervades even in food. Stop food facories, already young women and men of pakistan are carrying loads from these food factores by becoming obase. But local brown elites are so happy digging their graves with western foods to please food factory owners.
Good mr. Mr. Masadi.

Re: # 38 I am appaled by sloppy definition of derivative.
It is with horroe I read when dy= o. It goes against basic understanding. The derivative is simply rate of change of one function with respect to variable. Dy/dx is rate (ratio) of change of for small change of x. This small change is very small and you can make as small as possible but never equal to zero. arithmatically you can think and visualise increment in x can be 0.00000000001 but can not be zero as we can not divide by zero.
It my feeling as a amature tutor that different people learn different way. Many times its waste of time by tutor to go in classical definitions. As the students uses these tools and finds solving simple problems the ideas crystalize in young mind slowly and there is learn and digesting time and one can not rush through. Many time as students advance things not clear to him start clearing. This is learning process and is development. Initially crude or sloppy ideas is not problem and like rough diamond as students starts learning ang and thinking it slowly starts sparkling. The duty og good teacher to help and guide him and provide mental tools the student will cut himself like diamond cutter and will shine and delight to teacher. Just like in mine there are gems, sparkling stones and diamonds teacher should always keep in mine most is coal and should be happy as coal is powerful when you burn, he will become engineer and serve society.
Some people are not intelligent enough to grasp finer points but many things can be taught mechanically and in few terms they get essence as mathematics it self is tool to analyse and study things. But teacher with maths has more responsibility as some times even good student can have problem as language of mathematics some time itself is obstuse and difficult. A teacher should try to give practical and physical examples to make it simple and obvious. There is misunderstanding in areas of mathemtics studies masters are very difficult to understand, that is smoking something. People who have profound depth and wisdom in those areas ( there are teachers who have lots of information and no deep knowledge start show of talking obscure).have great ability to simply the discussion and remove fluff and go to essence. I always try to give examples while teaching and make tution seeker give his moneys worth.
For people who want to study cheaply if possible buy old times published russian subsidised , you will find them very cheap in old karachi books in used section.
They are translated and they are written in very sinpme language and most are complete text books.3 volumes on real analysis and one book on calculus of variations of variation with hard cover only 125 rs. The book sellers are very happy to get read of as now no body uses text book and class notes which are so sloppy and full of mistakes corrected appendix will be larger than books. I understand this is fast food time but people who wrote such garbage should be whipped.
I have not written here any thing supporting MASADI. So thete is chance it may get posted. Whenever I write anything supporting him it is rejected.
Good day and good luck.

Re: # 37 Mr. GT ...I will suggest all of you interested in what you are talking to understand to study basic course in Real Analysis. The book I can recommend is Real Analysis by mr. Goldberg. Writing here little blindly is fad but I know there much more to than that.
Have good day.

#36 Posted by AlephNull

Aleph Null, thanks a ton.

Iron,

I briefly skimmed through the paper you reference. I am a bit confused and so should read it more carefully when I have the time. What confuses me is the following:

Let n stand for null.

Axiom 9 (I believe) states that n=-n. But then n=0. In which case we are back to square one and there is nothing different.

So suppose there is something else. Now take axiom 6 (I believe) which states that for all a and b: a-b=a+(-b).

But then Axioms 6 and 9 imply that n=0 and again we are back to square one.

If you have read the paper do let me know what mistake I am making.

GT #34,

Goldblatt’s ‘Lectures on the Hyperreals’ in the Springer GTM series constructs basis analysis from the ground up without using epsilon-delta. There is also a very slim book by Edward Nelson, ‘Radically Elementary Probability Theory’, that develops probability theory using a minimal amount of nonstandard analysis. These are the only two books I have any acquaintance with – there may be many other good ones.

re: 34 and re:31
there is something called transreal numbers. You can check out a guy called James Anderson ( http://www.bookofparagon.com) who did some work in this area (some publications (http://www.bookofparagon.com/Mathematics/PerspexMachineVIII.pdf).
If you go to the website, he seems to have used this idea ofor developing what he calls a Perspex Machine and has developed some sort of a proof for this,.

There is a lot on wiki as well (but I would go a bit easy and sound a note of caution with the the wiki criticisms).
Check it out - who knows might just kindle some thing anew here.....

#31 Posted by AlephNull

Could you please recommend a basic reading on non-standard analysis. I have seen it being applied to a problem where essentially you have to join the two closest points opposite an infinitely small hole (non-convexity)in a particular way. The text was very intimidating for me.

#25 Posted by freethinker:

Dear Dr. Gill,

This is my last post on the particular example. You write:

"In this particular case, one doesn't need to use any limiting value of x because delta y = 0 for all values of x. y = constant is a straight line parallel to the x-axis; its gradient (dy/dx) is zero for all values of x."

I am sorry but you do not seem to get my point. IF the gradient is defined as dy/dx, then it is NOT AT ALL CLEAR that the gradient is zero for ANY x (forget all x). This is because delta x needs to converge to zero for dy/dx to have meaning. WITHOUT the concept of limit, dividing by zero would leave things UNDEFINED (see Aleph Null's #31, and an earlier post by khurram). Convergence to zero is very different from zero (see iron mask's beautiful example in #15).

Regards.

Gill writes "There is no short cut"

Of course there is a short cut for everything in the Prozac nation aka USA. Take a pill and it is supposed to fix everything, send a couple hundred dollars and out pops a PhD. And then we have "scholars" like you who spit out in tape recorder fashion what other books have already said or other people have said in "high school of the rote tradition" manner without any thought whatsoever. Then you read my report on the state of education in Pakistan and the "rote methodology", censor that article and write your own article titled "Rote Learning..." come on man, get real, perverts don't come in any purer form than yours...ahh but there was MAJ, he doomed us all to misery, made us politically weak, and then many more than us in India, you cannot approach that level of perversion...sorry my bad...

The status of infinitesimals – quantities that are smaller than any positive real number but not zero - was a thorn in the side of mathematicians for more than a century. Their use seemed problematic even though they were being employed to derive results that were seen to be obviously correct. Newton was so worried about the shaky foundations of the infinitesimal calculus that he had invented, that he used classical geometry to prove, in the Principia, results that he had obtained via calculus. An 18th century churchman, Bishop George Berkeley, launch a broadside against mathematicians, asking why, if they could accept and do business with such dubious notions, they could not accept the truths of revealed religion. It was left for Cauchy in the 19th century to put infinitesimal calculus on a rigorous foundation using the idea of limits.

There is however a 20th century approach to this problem – non-standard analysis, pioneered by the late Abraham Robinson - which shows that arithmetic with infinitesimals can be put on a logically sound footing. It is based on the observation that, as a consequence of the incompleteness of arithmetic, we can adjoin ‘nonstandard’ natural numbers – numbers all of which are larger than any standard natural number – to the natural number line without any inconsistency. Infinitesimals can then be defined as reciprocals of nonstandard natural numbers and we can proceed from there. Nonstandard analysis can be used to provide slick derivations of results whose traditional proofs are unwieldy.

IB "I happened to check your blog - and I fail to get the proof! what excatly is your point?"

You wouldn't know, after all is said and done he asks if Laila was male or female...perverts with a pea brain that believe in a rote monger like Gill wouldn't know...

In #28 read " majority collectively towards a minority because of the greed of one man"

as " majority collectively punishing a minority because of the greed of one man

Manto writes "Is this guy Masadi for real?"

Yes, I am for real and I am the worst nightmare of a-holes of the West that want to perpetuate the same old MAJ BS in this country to take it further down into the gutter than even what it is in right now. What I do know for sure is that the fate of the Indian Muslim was a direct consequence of the majority collectively towards a minority because of the greed of one man, the MAJ BS, a reaction to obtaining a non-viable country that was to become a whore of the West, thus causing debilitating suffering to the Muslims of this region both inside and outside India.

Today, I had to get some papers Xeroxed, so I went to a corner shop. This guy walks in and asks the shopkeeper, "When is Shab e Miraaj?" The shop keeper says, "People of an enslaved nation do not partake in these things, I am worried about load shedding and you are asking me this question. People who are enslaved cannot have a religious identity." Then he turned to me and said, "kyun saab jee, theek baat hey?"

I said "bilkul theek" and I am happy that the people of this nation are finally waking up. Then they guy who asked the "Miraaj" question asked the shopkeeper, “Then why did Quaid e Azam make Pakistan", and the shop keeper says, "Quaid e Azam ney jhak maree thee". I laughed as I left the shop on whose wall was the "jhak man's" photograph and said, " Soon the people of this nation will rise up against the BS of both the Quaid and the Mullah variety, enough is enough, the time of our liberation is nigh, one that involves social justice for all". No lackeys of the West like the MAJ will be tolerated, new currency will be printed. Enough of the same old BS. The High Priest of the Church of MAJ and all its franchises and whore houses will be shut down. Then will the humanity in Pakistan rejoice......Inshallah!

Kaptain: #26

I don't really know much about your situation, e.g., your background, etc. I may say one thing though. If you're not sufficiently knowledgable in mathematics, it's not the end of the world. There are other intellectually creative fields also. For instance, there is poetry. But if you must come back to mathematics, I suggest you should read some books on the history of development of mathematics. Two of such books which I read and found inspiring are as follows:

1. Mathematical Thught From Ancient to Modern Times (in 3 volumes), by Morris Kline.
2. Men of Mathematics, by by E.T. Bell.

These books provide a background on the kinds of problems which inspired great mathematicians. If after reading these books, you feel that you should know more about mathematics itself, you should take suitable courses at some college to learn. There is no short cut. If you start with applied mathematics instead of pure mathematics, you might be able to sustain your interest better. Mathematics is dry but for those who are really into it, it is simply beautiful.

Wishing you well,

Mohammad Akram Gill

Couldn't develop the passion for maths, it was made to look dreadful.

Any ideas, Mr. Gill, how can I make a comeback to Maths? Its been years I've been through it. But its the logic of nature.

GT: #23
In this particular case, one doesn't need to use any limiting value of x because delta y = 0 for all values of x. y = constant is a straight line parallel to the x-axis; its gradient (dy/dx) is zero for all values of x.
Mohammad Akram Gill

Which board, GT? I will look it up right now. Thanks.

#22 Posted by freethinker:

Gill, no I agree that your point is broader and I appreciate your point. As far as my point 2 is concerned, of course it can be proved given the definition of a limit. My earlier point was that we could at times intuitively understand dy/dx without going into the fundamentals.

Cheers.

GT: #12
I used dy/dx just as an example to make a point. I purposely stayed away from the beautiful (Calculus is indeed a very beautiful branch of mathematics) intricacies of calculus because the topic of my article was much broader. However, in your example #2, we do not necessarily need to believe intuitively that dy/dx = 0, it can be actually proved that dy/dx = 0 when y is a constant.
I was hoping that some young readers might share their experiences as students regarding rote learning. In my time in Pakistan, quite a bit of teaching was also by rote.
Wishing you well,
Mohammad Akram Gill

#19 Posted by KaalChakra:

Kaal:

Did you get to see the "quote"? I posted it sometime back in one of the boards.

Iron (with due apologies to Gill for the deviation):

Two things:

1. Asadi is a thinking man, a bit short-tempered. It would be worthwhile if you could be nice to him. There is a lot beyongd math.

2. Since you are interested. Do you know that all integrals under the chi-square distribution are approximations done with polynomials! Check it out. As an exercise try doing your own approximation using say 'mathematica'. Your approximations would be much sharper than chi-square tables published in the 60s (at the boundaries). Keep the degree at 1.

Still, GT, don't you love iron's 'visualizing' approach? If he tried hard enough, he might even be able to 'visualize' -3/2! :)

For the rest of us, mathematics indeed is the language of gods, not to be confused totally for anything mundanely 'real'. In that sense, jayp"s (#1) approach has an appeal.

#15 Posted by iron_mask:

"we can see the significance of this wrt to a the number lines! "

Perhaps. But I find it very difficult to understand "negative numbers" and therefore by extension the number line. Perhaps, one can try to understand it as "negation"(as used in logic). If so then we can 'understand' what -(3/2) is. As such we can use "equivalence" to understand what 3/(-2) is. But on its own 3/(-2) is a difficult concept. I, at least, won't be able to explain it to my daughter.

#15 Posted by iron_mask:

Iron:

At the apex (of the tent map) we have non-differentiability not dis-continuity. But your example of the curvature as an approximation is very nice indeed. As the approximation becomes sharper and sharper what do we get:

We get differentiability at the limit! But in truth at the apex we have non-differentiability.

Excellent example!

Masada Complex you are a sorry case of a man.

You give the mentally disabled people a bad name.

You stink.

Get lost.

Re: # 12

This is a problem which many face. If we start of with a gradient

Grad= (y1-y2)/(x1-x2)

if it is a straight line it is a constant. If it it is tent like function (couldnot resist the temptation GT!), then the magnitude of Grad remains the same, there is a sign change as we cross the apex (ofcourse assuming the tent is symmetric).

Now add a cruvature to the apex - thus is it no longer a point but a gradual change (note - above I have not considered the fact that the apex is a point of discontinuity). You will find that Grad is no longer a constant as we approach the top. AS we approach the top we have to take smaller and smaller steps (i.e (x1-x2) approaches epsilon) only then will we get an accurate measure / value for Grad. (we get a series of tangents). Again this would be syymetric. The problems becomes even more accute if instead of a smooth quadratic type curve at the apex we change it to a higher-order polynomial. At this point, how small should epsilon be becomes the question - indeed Grad might have to take on instantaneous values. In a way dy/dx is like that - an instanteneuous value. This is more clearly understood if we take velocity into consideration - where we can talk of instantaneuous velocity (not speed). dS/dt is a vector (note the above on sign changes), it provides us with information on speed and direction. If distance travelled is a staright line we get one value. If distance travelled is plooted against time and its a curve you get speed (if we are not interested in direction) but just magnitude, velocity (speed and direction (this need not be direction of travel but could be normal to it)), and acceleration as well!.

You say

1. We do not quite understand what 3/(-2) means. Yet we may use it as a 'step' to 'solve' a simple linear equation whose solution we understand quite well.

Clearly if we reqrite this as
(3-0)/0-2)
we can see the significance of this wrt to a the number lines! Am I wrong?

for your (2) see the instantaneous thing above - dx=x1-x2 = epsilon (epsilon small but greater than zero.)

who knows.....god knows!

#5 Posted by masadi

Asadi sahib:

Aap bohot gusse mein ho. I think you are pissed with Gill sahib for the wrong reasons. Even if the reasons were to be true they do not merit so much of anger. If you were to calm down (after all chowk is just a chowk), and communicate with Gill, both Gill and you could have good discussions from which many of us can learn some.

#4 Posted by khurram:

Kurram sahib,

You do not forget do you? :) But you should go a bit easy on khuram. There are several mathematecians with only one degree of separation from khuram. These are the ones who find it very difficult to accept the application of Zorn's Lemma (and hence the Axiom of Choice) in proofs.

Dear Gill,

It was a very nice read. Limiting approximations are actually quite difficult to fathom. Hence I, like you, believe it could be difficult for a person to understand phenomena if the person were to start from fundamentals (I may be wrong). For example, in dy/dx, where say y=f(x), delta x is never "actually" zero! Yet we can intuitively 'understand' (visualize) limits quite well and use dy/dx to verify other intuitions (hypotheses) that we may have. Let me give you 2 examples:

1. We do not quite understand what 3/(-2) means. Yet we may use it as a 'step' to 'solve' a simple linear equation whose solution we understand quite well.

2. Let y=constant for all x, and forget the definition of a 'limit' for the time being. Why choose 0 as the value of dy/dx if delta x were indeed to be equal to zero. Yet intuitively we have no problem with our choice as deltay/delta x would indeed be 0 no matter how 'small' delta x is.

Of course there are problems with this approach and the problems usually manifest when we integrate instead of differentiate. My view is that integration should be taught from first principles instead of teaching it as some sort of "inverse of the differential" as is often done. Would like to know your views on this.

Again nice read.

Re: # 8 -
masadi aka 'joker' - with every snide comment you make - I believe more in Mohammad Gill Sahab ( I am sure everyone else will agree ) .
I happened to check your blog - and I fail to get the proof! what excatly is your point?
kindly ( I am sure your can't be kind to anyone ) but for the sake of the forum - do email your content and whatever proof you have to the chowk staff and I'm sure they will respond and take action .
Here I would like to request Mohammad Gill Sahab to come up with his version .

Is this guy Masadi for real? If this is the state of the educated, god save the rest of us.

Is this guy Masadi for real? If this is the state of the educated, god save the rest of us.

IB writes " if you don't I wish I could punch you now "

Look you little rat, my article was submitted months ago and was censored by this a-hole. Regarding proving myself, you can read that article and the date on which it was published at the alternative site http://articles.asadi.org

As for my claims about the "parrot" mentality of Gill, read my comments on his 1001 previous articles. The guy can't think worth a fart....

Re: # 5
masadi
you are wrong gill sahib is not the editor.
the editor is an Indian P**** and she has over dozen nics.

Re: # 5 - masadi - I had a fair idea about you as a 'as*****' - now its confirmed!
kindly prove - what you said about a respected person - whom I had been reading from almost 6-7 years or more I guess! if you don't I wish I could punch you now .

Gill writes " was inspired to write this article by an interview of Professor Eric Mazur, Gordon McKay Professor of Applied Physics at Harvard"

The guy is a liar, my article which the GOP is now adopting, which I submitted to Chowk earlier this year, and which this pervert censored talked about the rote learning methodology and its origins and effects in Pakistan. The guy evidently read it, censored it and then composed his own piece of bs. Like I have been writing before about this person he merely reproduces what he has read in books without any iota of thought involved in it, and then claims to relate his "teaching methodology" to real life experiences. He is a tape recorderesqe, parrot, rote spitting out "scholar". All he is interested in is self promotion and abusing his office of editor at Chowk. People like him are a miserable disgrace to the world of education.

Where is our friend khuram (with the single 'r')? He would have loved this stuff about dy/dx .

Rote learning is something which I feel is being passed on from generation to generation. During my four year 'ordeal' in an engineering university, I was constantly surrounded by people whose attitude towards serious study was rather retarded. They believed strongly in rote learning, in obtaining better marks so that they could get better job opportunities in places where employers are more interested in your detailed marks certificate, and not in what you have learned. A terrible outcome of this easygoing laidback sort of attitude which has been passed on from generation to generation of students is the reduced number of engineering graduates who really are engineers, and not just exam clearing experts.

I believe that this problem has to be corrected at the grassroots level. The way you manage an institution and create an environment of learning is very important for young impressionable minds. Without a properly managed system, idle teachers, century old books and notes, the students would feel unimportant, as if they are here to merely go through the course, clear the exams, and get a job. This results in change in attitude of the students, and they feel lost. The students too should root out the ills and the traditions that have plagued engineering institutions and should try to make themselves better.

The problem is of ATTITUDE.

It is of WORLD VIEW.

Because a true and pure momeen can never suspend his belief and start theorizing- he would only work to save his books and faith. That is why the Islamic Republics strive to save the Qurans and Hadiths by insisting that all laws , including laws of physics, should be made to conform to Quran and Hadiths and should be Islamized. That is why the we see Islamic Sciences , Islamic Physics, Islmaic Chemistry, Islamic Psychology , Islamic Democracy and Islamic Republics.

So, any one who is a believer in all the stories about Allah, Prophet, Jinns, Houries, Jannah and Jahannum 'without-a-sense-of-dis-belief ' can ever think about theorizing about world imploding without the help of Allah???

The problem of rote learning has more to do with finality of knowledge that is insited upon in third world countries like Pakistan.

The problem is with the entrenched religious theologies like mullah Islam.

unless and until we root out these theologies of hate we can never see any progress in sciences.

Gill saab,

Your article is very interesting, it talks about the links between maths and physics.

I was taught very differently, I was told that mathematics teaches you to think in abstract terms, any attempts to make a physical linkage will only limit your learning. Difficult to think in more than 3 dimensions, and well you are stuffed in dealing with vectors.

dy/dx is an operator, it has some rules and that is it, there is no physical interpretation. Mathematics is a system of logic, and there are operators, plus minus to del and integrals and transforms and you name it.

The physical ideas linked to maths is very limiting, may be should be left to hydraulics. Maths is simply a language for abstract thinking.